Earliest Known Uses of Some of the Words of Mathematics (J)

Last revision: Oct. 28, 2018

J-SHAPED is found in 1911 in An Introduction to the Theory
of Statistics by G. U. Yule (David, 1995).

JACKKNIFE in Statistics. David (1995) gives Rupert G. Miller’s "A Trustworthy Jackknife,"
Annals of Mathematical Statistics,35 (1964), 1594-1605 as the first
published use of the term. Miller explains that John W. Tukey had adopted the term
because "a boy-scout’s jackknife is symbolic of a rough-and-ready instrument capable of
being utilized in all contingencies and emergencies." M. H. Quenouille, in "Notes on
Bias in Estimation" Biometrika,43, (1956), 353-360, had written colourlessly
of a procedure for supplying "an approximate correction for bias" [John Aldrich].

The term JACOBIAN was coined by James J. Sylvester
(1814-1897), who used the term in 1852 in The Cambridge & Dublin Mathematical
Journal.

Sylvester also used the word in 1853 "On a Theory of the Syzygetic Relations of Two Rational Integral Functions,
Comprising an Application to the Theory of Sturm’s Functions, and That of the
Greatest Algebraical Common Measure," Philosophical Transactions of the Royal Society of London,
CXLIII, Part III, pp. 407-548: "In Arts. 65, 66, I consider the relation
of the Bezoutiant to the differential determinant, so called by Jacobi, but
which for greater brevity I call the Jacobian."
C. G. J. Jacobi’s
(1804-1851) paper was
De determinantibus functionalibus (1841).

JEFFREYS PRIOR. In 1946 Harold Jeffreys published "An Invariant
Form for the Prior Probability in Estimation Problems," Proceedings of the
Royal Society, A, 186, 453-461. He incorporated the material in the
second edition of his Theory of Probability (1948). The expression "Jeffreys
prior" (or variants of it) became established in the 1960s; see e.g. Bruce
M. Hill "The Three-Parameter Lognormal Distribution
and Bayesian Analysis of a Point-Source Epidemic," Journal
of the American Statistical Association, 58,
(1963), 72-84 or J. Hartigan "Invariant Prior Distributions, Annals of Mathematical
Statistics, 35, (1964), 836-845.

JERK was used by J. S. Beggs in 1955 in Mechanism iv.
122: "Since the forces to produce accelerations must arise from
strains in the materials of the system, the rate of change of
acceleration, or jerk, is important" [OED].

In English the term is found in 1889 in A Treatise on Linear Differential Equations Volume I by Thomas Craig.
The table of contents has “Jordan’s Canonical Form of the Substitution corresponding to any Critical Point.” [Google print search by James A. Landau]

JORDAN CURVE appears in W. F. Osgood, "On the Existence of the
Green’s Function for the Most General Simply Connected Plane Region,"
Transactions of the American Mathematical Society, Vol. 1, No.
3. (July 1900): "By a Jordan curve is meant a curve of the
general class of continuous curves without multiple points,
considered by Jordan, Cours d'Analyse, vol. I, 2d edition,
1893..." [OED].

JORDAN CURVE THEOREM is dated 1915-20 in RHUD2.

Jordan curve-theorem is found in D. W. Woodard, "On
two-dimensional analysis situs with special reference to the Jordan
curve-theorem," Fundamenta (1929).

Julia set is found in English in 1976 in the
Canadian Journal of Mathematics 28/1211: “We
consider now those Julia sets which are sets of non-uniqueness and hence are very far from being Weierstrass sets.” [OED]